Question

Rewrite 5/2x-8 - 1 = 9. Which of the four answers are correct?

x ≠ 4
x ≠ -8
x ≠ -4
x ≠ 8

Answer 1

Let's start by rewriting the equation \( \frac{5}{2}x - 8 - 1 = 9 \).

1. Combine like terms on the left side:
\[
\frac{5}{2}x - 9 = 9
\]

2. Add 9 to both sides:
\[
\frac{5}{2}x = 18
\]

3. Multiply both sides by \( \frac{2}{5} \) to solve for \( x \):
\[
x = 18 \times \frac{2}{5} = \frac{36}{5}
\]

Thus, \( x = \frac{36}{5} \).

Now, we need to analyze the given constraints:

- \( x \neq 4 \)
- \( x \neq -8 \)
- \( x \neq -4 \)
- \( x \neq 8 \)

Since \( \frac{36}{5} = 7.2 \), it is not equal to 4, -8, -4, or 8. Therefore, all four conditions listed are satisfied.

The correct interpretations of the constraints would be:

- \( x \neq 4 \) (Correct)
- \( x \neq -8 \) (Correct)
- \( x \neq -4 \) (Correct)
- \( x \neq 8 \) (Correct)

In conclusion, all four conditions are correct since \( x \) does not equal any of these values.